Second order DE

Which method can i use to solve u'' - (t-1)/t u' = t/(t+1)??

This is an equation I have formed by making it U absent and I let p = dy/dx and dp/du = d^y/dx^2 but then i'm stuck after that -.-"" any help would be appreciated I've attempted this question so many times...I tried using an integrating factor to solve but i couldnt do it..

Right. The middle term is the tricky one. In fact, it's so hard it's easy (if you know the result, that is).

The middle integral gives you what's called the exponential integral function. In fact, there is no elementary antiderivative. So your final solution is just going to have to include that term unsimplified. Incidentally, wolframalpha has the exponential integral term in its solution if you just go from scratch with the DSolve command.

Don't forget also that you have to integrate one more time to get to u. I wouldn't bother trying to integrate the exponential integral function. Just write out the integral.